Results 151 to 160 of about 13,841 (198)

Application of the Fractional Sturm–Liouville Theory to a Fractional Sturm–Liouville Telegraph Equation

Complex Analysis and Operator Theory, 2021
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Ferreira, M., Rodrigues, M. Manuela, Vieira, Nelson   +2 more
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Sturm--Liouville theory for the p-Laplacian

Studia Scientiarum Mathematicarum Hungarica, 2003
A version of Sturm--Liouville theory is given for the one-dimensional p-Laplacian including the radial case. The treatment is modern but follows the strategy of Elbert's early work. Topics include a Prüfer-type transformation, eigenvalue existence, asymptotics and variational principles, and eigenfunction oscillation.
Binding, P., Drábek, P.
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Sturm Liouville eigenvalue theory

2014
In this chapter we deal with Dirichlet boundary value problems as $$\left\{ {\begin{array}{*{20}{r}} {\begin{array}{*{20}{c}} {x''\left( t \right) + A\left( t \right)x'\left( t \right) + B\left( t \right) + x\left( t \right) + \lambda C\left( t \right)x\left( t \right)}&{ = 0} \end{array}}\\ {\begin{array}{*{20}{c}} {x\left( a \right)}&{ = 0} \end ...
Shair Ahmad, Antonio Ambrosetti
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Sturm-Liouville Theory

1990
1. In a series of articles dating from 1836–1837, Sturm and Liouville created a whole new subject in mathematical analysis. The theory, later known as Sturm-Liouville theory, deals with the general linear second-order differential equation $$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$ (1) with the imposed ...
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More Sturm–Liouville Theory

2014
In Theorem 23.6, the bifurcation theorem for nonlinear Sturm–Liouville eigenvalue problems Lu = F (sBC) that concluded the previous chapter, a key hypothesis was the invertibility of \(Lu = -(pu')' + qu\) with respect to the given boundary conditions. Certainly a necessary condition for an operator to be invertible is that it be one-to-one.
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Sturm—Liouville—Theorie

1997
In diesem Kapitel werden wir Anfangs- und Randwertprobleme fur eine lineare gewohnliche Differentialgleichung 2. Ordnung mit variablen Koeffizienten in eine Integralgleichung umformen, sodas wir die Ergebnisse (insbesondere uber Eigenwerte) aus Kapitel 2 und 4 benutzen konnen. Auf einem Intervall [a, b] betrachten wir die Gleichung $$\bar{p}(s){x}''
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The Qualitative Sturm–Liouville Theory on Spatial Networks

Journal of Mathematical Sciences, 2004
The authors consider boundary value problems generated by the differential expression \[ -(p(x)y')'+q(x)y=f(x) \] on the edges of a graph domain. At the pendant vertices Dirichlet boundary conditions and at the vertices of degree greater 1 the continuity conditions together with Kirchhoff-type conditions are imposed.
Pokornyi, Yu. V., Pryadiev, V. L.
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Nonlinear Sturm–Liouville Theory

2014
In the next chapter, we’ll apply the Krasnoselskii-Rabinowitz bifurcation theorem in a very specific way: to the Euler buckling problem. The buckling problem belongs to an important class of problems in ordinary differential equations called nonlinear Sturm-Liouville problems.
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Fourier Analysis and Sturm-Liouville Theory

1998
The principal method for solving the boundary value problems of mathematical physics is the method of separation of variables. The method will be developed and applied to a variety of problems in this chapter and Chapter 9.
Grant B. Gustafson, Calvin H. Wilcox
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Sturm-Liouville theory for the radial $\Delta_p$ -operator

Mathematische Zeitschrift, 1998
Let \(s^{(p)}=| s| ^{p-1}s\) (\(s\) real). The differential operator \[ L_p^\alpha=r^{-\alpha}\bigl(r^\alpha{u'}^{p-1}\bigr)' \] is considered, where \(s\) is the independent variable, \(\alpha\geq 0\), and \(p>1\). For \(\alpha=n-1\) and \(r=| x| \), this is the radial \(\Delta_p\)-operator in \(\mathbb{R}^n\).
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